A slope-descending speed control device has been well known, which controls braking forces to control a deceleration of a vehicle during downhill traveling so that an actual vehicle speed conforms to a target vehicle speed by a PID feedback control executed in accordance with a difference between the target vehicle speed and the actual vehicle speed. For example, in the under-mentioned patent citation 1, a slope-descending speed control device is disclosed which is configured to modify the gains in a PID feedback control in accordance with a loading burden of a vehicle.